課程名稱︰物理化學一 課程性質︰必修 課程教師︰戴子安 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2011/12/5 考試時限（分鐘）：120 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(20 points) Explain the following terms. Use graphs if necessary. (a) entropy changes for a system and its surrounding. (b) Boltzmann hypothesis for entropy. (c) The 3rd law of thermodynamics. (d) Otto engine. (e) the fundamental equations of thermodynamics. (f) Maxwell relation. (g) the Gibbs-Helmholtz equation. (h) the Gibbs energy as a function of pressure for ideal and real gas. (i) at high pressure, the relation between the activity of a pure solid and pressure. (j) the Gibbs-Duhem equation. 2.(10 points) A sample of K(s) (potassium) of mass 2.38g undergoes combustion in a constant volume calorimeter. The calorimeter constant is 1849(J/K), and the measured temperature rise in the inner water bath containing 1450g of water is 2.91K. Calculate ΔUf°and ΔHf°for K20(s) (potassium oxide) The molar mass of the element potassium is given as 39(g/mol) 3.(10 points) Calculate ΔS, ΔS(surrounding),ΔS(total) and when the volume of 123g of CO (MW = 28) initially at 298K and 1bar increase by a factor of four in (a) an adiabatic reversible expansion, (b) an expansion against vaccum, (c) an isothermal reversible expansion. _ Take Cp to be constant at the value 29.14(J/mol) and assume ideal gas behavior. State whether each process is spontaneous. The temperature of surrounding is 298K. 4.(10 points) For a VDW gas, its fugacity has a simple expression if only the 2nd virial coefficient is used. To this degree of approximation, derive the _ _ _ _ _ _ expression for G, S, A, U, H, V. 5.(10 points) Derive the efficiency,ε for an Otto engine. 6.(10 points) Calculate the change in entropy when 100g of (a) water at 0℃ (b) ice at at 0℃ in an insulated container. 7.(10 points) Calculate the maximum non-expansion work that can be obtained from the freezing of supercooled water at -20℃ and 1.0 atm and ρwater = 0.999(g/cm^3), ρice = 0.917(g/cm^3), _ _ Cp(water) = 75.3(J/K*mol), Cp(ice) = 36.8(J/K*mol), _ and Δ(fus)H°= -6004(J/mol) (water at 0℃) (some of these information are used in question 7) 8.(20 points) _ _ (a) For a van der Waals gas, derive the relation for Cp - Cv, _ δH (b) For a VDW gas, derive the expression for its (----) δP (T), A δ(---) T (c) Show [--------] = U 1 (V) δ(---) T δP (d) Show that TdS = CvdT + T(-----) dV δT (V) --

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